Question

The harmonic mean of two numbers is $\frac{1}{18}$. One of the numbers is $9$. What is the other number?

• A. $14.88$
• B. $17.88$
• C. $15.88$
• D. $12.66$

Answer 1

The correct option is B $17.88$

We know harmonic mean $=$ $\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}...+\frac{1}{x_n}}$
Here $n=2$
Therefore, $\frac{1}{9}=\frac{2}{\frac{1}{9}+\frac{1}{x}}$
$\Rightarrow 18=\frac{x+9}{9x}$
$\Rightarrow 162x-x=9$
$\Rightarrow x=17.88$